Related papers: Information geometry of perturbed gradient flow sy…
In graphene, where the electron-electron scattering is dominant, electrons collectively act as a fluid. This hydrodynamic behaviour of charge carriers leads to exciting nonlinear phenomena such as solitary waves and shocks, among others. In…
Flow instability and turbulent transition can be well explained using a new proposed theory--Energy gradient theory [1]. In this theory, the stability of a flow depends on the relative magnitude of energy gradient in streamwise direction…
In this work, we study non-Newtonian fluid flow in heterogeneous porous media. We are interested in fluids presenting a specific change in rheology: Newtonian below a certain shear rate and power law above. Since porous media generally…
Stochastic geometric mechanics (SGM) is known for its potential utility in quantifying uncertainty in global climate modelling of the Earth's ocean and atmosphere while also preserving the fundamental advective transport properties of ideal…
We discuss a link between graph theory and geometry that arises when considering graph dynamical systems with odd interactions. The equilibrium set in such systems is not a collection of isolated points, but rather a union of manifolds,…
We developed a general deep learning framework, FluidGAN, capable of learning and predicting time-dependent convective flow coupled with energy transport. FluidGAN is thoroughly data-driven with high speed and accuracy and satisfies the…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…
Information geometry provides differential geometric concepts like a Riemannian metric, connections and covariant derivatives on spaces of probability distributions. We discuss here how these concepts apply to quantum field theories in the…
The observation of fluid-like behavior in nucleus-nucleus, proton-nucleus and high-multiplicity proton-proton collisions motivates systematic studies of how different measurements approach their fluid-dynamic limit. We have developed…
A new geometric approach to systems with boundary energy flow is developed using infinite-dimensional Dirac structures within the Lagrangian formalism. This framework satisfies a list of consistency criteria with the geometric setting of…
We consider the dynamics of vector fields on three-manifolds which are constrained to lie within a plane field, such as occurs in nonholonomic dynamics. On compact manifolds, such vector fields force dynamics beyond that of a gradient flow,…
In ultra-clean 2d materials electron viscosity is as important as Ohmic dissipation and electron transport exhibits hydrodynamic features. Using a simple framework of Brinkman equations we find that hydrodynamic electron flows exhibit a…
In this article, we continue the program started in our previous article of exploring an important class of thermodynamic systems from a geometric point of view. In order to model the time evolution of systems verifying the two laws of…
Modern energy systems in vehicles and built infrastructure are governed by high-dimensional dynamics spanning multiple physical domains (e.g., electrical, thermal, mechanical) and timescales. This tutorial paper presents a graph-based…
Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision, including view-point in activity analysis, articulation in shape analysis, and measurement invariance in…
A nonlinear parabolic equation of sixth order is analyzed. The equation arises as a reduction of a model from quantum statistical mechanics, and also as the gradient flow of a second-order information functional with respect to the…
A turbulent flow is maintained by an external supply of kinetic energy, which is eventually dissipated into heat at steep velocity gradients. The scale at which energy is supplied greatly differs from the scale at which energy is…
In this work we compare two fundamentally different approaches to the electronic transport in deformed graphene: a) the condensed matter approach in which current flow paths are obtained by applying the non-equilibrium Green's function…
In many physical situations involving diverse length scales, waves or rays representing them travel through media characterized by spatially smooth, random, modest refactive index variations. "Primary" diffraction (by individual…
We propose and construct a two-parameter perturbative expansion around a Friedmann-Lema\^{i}tre-Robertson-Walker geometry that can be used to model high-order gravitational effects in the presence of non-linear structure. This framework…